Parameter estimation of oscillatory systems (with application to circadian rhythms)

Abstract

Oscillatory behavior is an important and integral in cellular and physiological functions, with examples from cell cycle to circadian rhythms and others. With the explosion of biological data, there has been a shift toward systems oriented approach in biology through the creation of mathematical models and the application of mathematical analysis. These models are reverse engineered from experimental data through model identification and parameter estimation procedure, borrowing many concepts and tools from engineering field. Though the literature on model identification is already mature, the identification of oscillatory systems however is not yet routine, due to the relatively low importance of oscillations in engineering systems. This thesis aims to fill this gap by establishing a parameter estimation framework for oscillatory systems that facilitates data reconciliation between model prediction and experiments. The proposed methodology was tested on model identification of <em>Drosophila</em> circadian gene regulatory network.